On a Unified Mittag-Leffler Function and Associated Fractional Integral Operator

Yanyan Zhang, Ghulam Farid, Zabidin Salleh and Ayyaz Ahmad

Mathematical Problems in Engineering, 2021, vol. 2021, 1-9

Abstract:

The aim of this paper is to unify the extended Mittag-Leffler function and generalized Q function and define a unified Mittag-Leffler function. Both the extended Mittag-Leffler function and generalized Q function can be obtained from the unified Mittag-Leffler function. The Laplace, Euler beta, and Whittaker transformations are applied for this function, and generalized formulas are obtained. These formulas reproduce integral transformations of various deduced Mittag-Leffler functions and Q function. Also, the convergence of this unified Mittag-Leffler function is proved, and an associated fractional integral operator is constructed.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:6043769

DOI: 10.1155/2021/6043769

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